Giải thích các bước giải:
Ta có:
$f(x)=ax^2+bx+c$
$\to f(x)=a(x^2+\dfrac{b}{a}x)+c$
$\to f(x)=a(x^2+2\cdot x\cdot \dfrac{b}{2a}+(\dfrac{b}{2a})^2-(\dfrac{b}{2a})^2)+c$
$\to f(x)=a((x+\dfrac{b}{2a})^2-\dfrac{b^2}{4a^2})+c$
$\to f(x)=a(x+\dfrac{b}{2a})^2-\dfrac{b^2}{4a}+c$
$\to f(x)=a(x+\dfrac{b}{2a})^2-\dfrac{b^2-4ac}{4a}$
$\to f(x)=a((x+\dfrac{b}{2a})^2-\dfrac{b^2-4ac}{4a^2})$
Khi $\Delta\le 0\to \dfrac{b^2-4ac}{4a^2}\le 0$
$\to (x+\dfrac{b}{2a})^2-\dfrac{b^2-4ac}{4a^2}\ge 0$
$\to f(x)$ có cùng dấu với $a$
